The Basics of Landscape Composition by Diane Johnson
This article is about painting, but it's applicable to the photography.
Photo Technique by James Gentles
Good description of golden rules.
Rule of Thirds by Edwin Leong
Photography e-Book, chapter 15. Several advices.
The Golden Ratio by Edwin Leong
Photography e-Book, chapter 16. Interesting description.
Lessons in Composition for the Amateur Photographer by Dale Cotton
This part is about "Rule of Thirds".
Proportions: Theorie and Construction by Volker Muller
Explained the mathematical rules of Golden Mean, Modulor, and Square Root of Two.
Composition by Michael Minner
Portrait photography and the Rule of Thirds.
Finding a satisfactory format for a square canvas by John Hagan
Photography, the Golden Mean, and Geeky Coolness by Laurie Nyveen
Several short examples.
Golden Section and Photography by Eugene Ilchenko
Several examples and photo-adjuster tool to help to adjust the composition.
Creativity and the Rule of Thirds by Jim Altengarten
Good article with description and examples.
The Rule of Thirds by John Longenecker
Description of the Rule of Thirds as well as a lot of related links.
The Golden Mean by Stuart Low
Natural and mathematical rules and how they have been applied in design.
Space, Figure, and Ground Lesson by Petteri Sulonen
The objective of this lesson is to introduce three fundamental elements in compositional thinking.
Composition Basics lesson by Michael Fodor
General principles of the Rule of Thirds and the Golden Mean as well as several composition advises.
Rule of Thirds lesson by Michael Fodor
Examples of the Rule of Thirds.